arXiv subjects

Eugeny Babichev

Publications and source records attributed to Eugeny Babichev.

At least 19 recordsLinked to original sources

arXiv2026

Extending Weinberg's EFT: effective scalar-tensor theories up to sixth order

We present a systematic construction of the six-derivative effective scalar-tensor theories, extending the four-derivative framework previously developed by Steven Weinberg. The on-shell effective field theory comprises five parity-even and three parity-odd independent six-derivative scalar-tensor interactions, representing all inequivalent deformations consistent with general covariance. We further confirm this operator counting through an independent analysis using the scattering amplitude formalism in four-dimensional flat spacetime. The six-derivative Lagrangian constructed here provides the next-to-leading-order extension of scalar-tensor gravity, furnishing a robust framework for exploring quantum or stringy corrections, parity-violating interactions, and strong-curvature effects in cosmology, black hole physics and gravitational wave observations.

hep-th↗

arXiv2026

Towards Gravitational Wave Turbulence within the Hadad-Zakharov metric

The theory of gravitational wave turbulence describes the long-term statistical behaviour of a set of weakly nonlinear interacting waves. In this paper, we aim to study aspects of gravitational turbulence within the framework of general relativity using the Hadad-Zakharov (HZ) metric. The latter is parameterised by four functions (the coefficients of a diagonal metric) that must satisfy seven non-trivial Einstein equations, six of which are independent. The issue of their mutual compatibility is therefore essential, yet it has so far been overlooked. In this work, we argue that these equations can be compatible in the weakly nonlinear regime under specific conditions. Our analytical investigation is complemented by direct numerical simulations performed with a new GPU-based code, TIGER. A comparative analysis of the evolution of the Ricci and Kretschmann scalars indicates that gravitational wave turbulence corresponds to the propagation of a genuine physical degree of freedom. These numerical findings, however, must be interpreted with caution, given the difficulty of satisfying all seven Einstein equations simultaneously with sufficient accuracy. On the other hand, our simulations reproduce well the expected properties of the wave turbulence regime, with the emergence of a dual cascade of energy and wave action, and for the latter the observation of the Kolmogorov-Zakharov spectrum. In addition, our analysis reveals that the canonical variables of the problem evolve towards a nearly Gaussian statistical distribution punctuated by intermittent coherent (spatially localised and long-living) structures. In contrast to the canonical variables, the structure functions of the gauge-invariant metric components exhibit monofractal behaviour, which is a classical property of wave turbulence.

gr-qc↗

arXiv2025

Cherenkov radiation as ghost instability

We demonstrate that Cherenkov radiation can be interpreted as ghost instability of a certain type. Solutions of modified gravity theories often contain ghost instabilities. One type of such ghost instability is associated with existence of different types of species with causal cones that do not share common time, which leads to vacuum decay via creation of particles with positive and negative energies. We show that this ghost instability can be seen as Cherenkov radiation and vice versa.

gr-qc↗

arXiv2025

Properties of general stationary axisymmetric spacetimes: circularity and beyond

We analyse properties of general stationary and axisymmetric spacetimes, with a particular focus on circularity -- an accidental symmetry enjoyed by the Kerr metric, and therefore widely assumed when searching for rotating black hole solutions in alternative theories of gravity as well as when constructing models of Kerr mimickers. Within a gauge specified by seven (or six) free functions, the local existence of which we prove, we solve the differential circularity conditions and translate them into algebraic relations among the metric components. This result opens the way to investigating the consequences of circularity breaking in a controlled manner. In particular, we construct two simple analytical examples of non-circular deformations of the Kerr spacetime. The first one is "minimal", since the horizon and the ergosphere are identical to their Kerr counterparts, except for the fact that the horizon is not Killing and its surface gravity is therefore not constant. The second is "not so minimal", as the horizon's profile can be chosen arbitrarily and the difference between the horizon and the so-called rotosurface can be appreciated. Our findings thus pave the way for further research into the phenomenology of non-circular stationary and axisymmetric spacetimes.

gr-qc↗

arXiv2025

Large black-hole scalar charges induced by cosmology in Horndeski theories

The regularity of black hole solutions, embedded in an expanding Universe, is studied in a subclass of Horndeski theories, namely the sum of the simplest quadratic, cubic and quintic actions. We find that in presence of a time derivative of the scalar field, driven by the cosmological expansion, this regularity generically imposes large scalar charges for black holes, even when assuming strictly no direct coupling of matter to the scalar field. Such charges cause a significant accretion of the scalar field by the black holes, driving its local time derivative to a small value. This phenomenon, together with the Vainshtein screening typical of these theories, strongly suppresses observable scalar effects. We show that this full class of models is consistent with LIGO/Virgo detections of gravitational waves, but that the LISA mission should be able to constrain the coefficient of the quintic term at the $10^{-30}$ level in a self-acceleration scenario, an improvement by 16 orders of magnitude with respect to what is imposed by the speed of gravitational waves.

gr-qc↗

arXiv2025

The cosmic trimmer: Black-hole hair in scalar-Gauss-Bonnet gravity is altered by cosmology

Static black holes in general relativity modified by a linear scalar coupling to the Gauss-Bonnet invariant always carry hair. We show that the same mechanism that creates the hair makes it incompatible with a cosmological horizon. Other scalar-tensor models do not have this problem when time dependence of the scalar provides a natural matching to cosmology. Scalar-Gauss-Bonnet gravity is particularly rigid, and such a scenario does not help. An extra operator makes the theory behave like the other models, and the cosmological horizon can be accommodated. The hair, however, is drastically altered.

gr-qc↗

arXiv2024

Horndeski speed tests with scalar-photon couplings

We revisit multi-messenger constraints from neutron star mergers on the speed of propagation of gravitational and electromagnetic waves in Horndeski and beyond Horndeski theories. By considering non-trivial couplings between the dark energy field and the electromagnetic sector, the electromagnetic wave can propagate through the cosmological background at non-unit speed, altering the phenomenological constraints on its gravitational counterpart. In particular, we show that recent models derived from a Kaluza-Klein compactification of higher dimensional Horndeski models fall into a broader class of theories disformally related to those whose gravitational waves propagate with unit speed. This disformal equivalence can, however, be broken by the gravitational couplings to other sectors with interesting phenomenological consequences. We also consider higher order couplings between the scalar and the photon with second order field equations, and show that they are not compatible with constraints coming from multi-messenger speed tests and the decay of the gravitational wave.

gr-qc↗

arXiv2024

Global conformal symmetry in scalar-tensor theories

We study a subclass of Horndeski gravity which has both global conformal and shift symmetries. Global symmetries are characterised by the presence of a conserved current which has been shown to be of particular importance for the integrability features of the theory at hand yielding numerous compact object solutions. We find the general conserved current associated to global conformal symmetry of Horndeski theories. We discuss some of its properties, how it can be conveniently broken by physically relevant terms and, show how it is related to that of shift symmetry when shift symmetry is present. Given our results, we consider a particular theory and demonstrate how the presence of symmetries provides integrability for the given black hole solution. We then find the charged extension of the solution thanks to the conformal invariance of the Maxwell action.

hep-th↗

arXiv2024

Testing disformal non-circular deformation of Kerr black holes with LISA

There is strong observational evidence that almost every large galaxy has a supermassive black hole at its center. It is of fundamental importance to know whether such black holes are described by the standard Kerr solution in General Relativity (GR) or by another black hole solution. An interesting alternative is the so-called disformal Kerr black holes which exist within the framework of degenerate higher-order scalar-tensor (DHOST) theories of gravity. The departure from the standard Kerr black hole spacetime is parametrized by a parameter $D$, called $\textit{disformal parameter}$. In the present work, we discuss the capability of LISA to detect the disformal parameter. For this purpose, we study Extreme Mass Ratio Inspirals (EMRI's) around disformal Kerr black holes within the framework of the quadrupole hybrid formalism. Even when the disformal parameter is very small, its effect on the globally accumulated phase of the gravitational waveform of an EMRI can be significant due to the large number of cycles in the LISA band made by the small compact object. We show that LISA will in principle be able to detect and measure extremely small values of the disformal parameter which in turn, can be seen as an assessment of LISA's ability to detect very small deviations from the Kerr geometry.

gr-qc↗

arXiv2024

Generalisation of Conformal-Disformal Transformations of the Metric in Scalar-Tensor Theories

We study new classes of metric transformations in the context of scalar-tensor theories, which involve both higher derivatives of the scalar field and derivatives of the metric itself. In general, such transformations are not invertible as they involve derivatives of the metric, which typically leads to instability due to Ostrogradsky ghosts. We show, however, that a certain class of this type of transformations is invertible: we construct new examples of invertible conformal (and also disformal) transformations with higher derivatives. Finally, we make use of these new transformations to construct extended mimetic theories of gravity, and we study their properties in the context of cosmology.

gr-qc↗

arXiv2023

Exact black hole solutions in higher-order scalar-tensor theories

In this chapter, we discuss explicit black hole solutions in higher-order scalar-tensor theories. After a brief recap of no-hair theorems, we start our discussion by so-called stealth solutions present in theories with parity and shift symmetry. Stealth solutions are such that their metric are Ricci flat General Relativity solutions, but they are accompanied by a non-trivial scalar field, in both spherically-symmetric and rotating cases. The stealth metrics then enable to construct an analytic stationary solution of scalar-tensor theory which is called disformed Kerr metric. This solution constitutes a measurable departure from the usual Kerr geometry of GR. We discuss within parity and shift symmetric theories several non-stealth solutions. We then consider scalar-tensor theories stemming from a Kaluza-Klein reduction of a higher-dimensional Lovelock theory. These theories encompass all Horndeski functionals and hence go beyond parity and shift symmetry. Reduction and singular limits allow one to obtain non-stealth black holes with differing interesting properties which are not Ricci flat metrics. We analyse the solutions obtained and classify them with respect to the geometry of the internal space according to their Kaluza-Klein origin.

gr-qc↗

arXiv2023

Rotating black holes embedded in a cosmological background for scalar-tensor theories

We present solutions of DHOST theories describing a rotating black hole embedded in an expanding universe. The solution is constructed by conformal transformation of a stealth Kerr(-de Sitter) black hole. The conformal factor depends explicitly on the scalar field -- but not on its derivative -- and defines the new theory. The scalar field of the stealth Kerr(-de Sitter) solution depends on time, leading to the time-dependence of the obtained conformal metric, with cosmological asymptotics at large distances. We study the properties of the obtained metric by considering regular null geodesic congruences, and identify trapping black hole and cosmological horizons.

gr-qc↗

arXiv2023

Selecting Horndeski theories without apparent symmetries and their black hole solutions

Starting from a generalised Kaluza-Klein action including arbitrary Horndeski potentials, we establish integrability and compatibility conditions that solve the generic field equations for spherical symmetry. The resulting theories can be identified as general Horndeski theories having no apparent symmetries in four dimensions or as effective string theory actions with an IR logarithmic running for the dilaton, higher order corrections and generalised Liouville type potentials. For such actions, we then find black holes with secondary hair parameterized by two coupling constants essentially characterising the theories at hand. One is related to an action which is conformally coupled in five dimensions while the second is related to a Kaluza-Klein reduction of Lovelock theory. We show that the full action can also be interpreted as a sum of conformally coupled actions in differing dimensions. Known solutions are mapped within the general chart of the found theories and novel general black holes are discussed, focusing on their important properties and some of their observational constraints.

gr-qc↗

arXiv2023

Conformally coupled scalar in Lovelock theory

In arbitrary higher dimension, we consider the combination of Lovelock gravity alongside a scalar-tensor action built out of higher order operators and Euler densities. The latter action is constructed in such a way as to ensure conformal invariance for the scalar field. For the combined version of these theories, we show the existence of black hole solutions interpreted as stealth configurations within Lovelock gravity theory. The scalar field solutions are endowed with an integration constant that may be identified as a scalar charge. In particular, we show that these stealth solutions can be extended to include a time-dependent scalar field despite the underlying theory being non shift-symmetric. Finally, we present a procedure to obtain a non-conformally invariant action in even dimensions from the considered theory. For the target theory, the scalar field is not conformally coupled to gravity although the scalar field equation itself is conformally invariant. By means of this procedure, the black hole stealth configurations are converted into non-stealth black hole solutions, as discovered recently in four dimensions.

gr-qc↗

arXiv2022

Shrouded black holes in Einstein-Gauss-Bonnet gravity

We study black holes in a modified gravity scenario involving a scalar field quadratically coupled to the Gauss-Bonnet invariant. The scalar is assumed to be in a spontaneously broken phase at spatial infinity due to a bare Higgs-like potential. For a proper choice of sign, the non-minimal coupling to gravity leads to symmetry restoration near the black hole horizon, prompting the development of the scalar wall in its vicinity. The wall thickness depends on the bare mass of the scalar and can be much smaller than the Schwarzschild radius. In a weakly coupled regime, the quadratic coupling to the Gauss-Bonnet invariant effectively becomes linear, and no walls are formed. We find approximate analytical solutions for the scalar field in the test field regime, and obtain numerically static black hole solutions within this setup. We discuss cosmological implications of the model and show that it is fully consistent with the existence of an inflationary stage, unlike the spontaneous scalarization scenario assuming the opposite sign of the non-minimal coupling to gravity. Our model predicts the speed of gravitational waves to be extremely close to unity, - in a comfortable agreement with the observation of the GW170817 event and its electromagnetic counterpart.

gr-qc↗

arXiv2022

Conformally coupled theories and their deformed compact objects: from black holes, radiating spacetimes to eternal wormholes

We study a higher order conformally coupled scalar tensor theory endowed with a covariant geometric constraint relating the scalar curvature with the Gauss-Bonnet scalar. It is a particular Horndeski theory including a canonical kinetic term but without shift or parity symmetry for the scalar. The theory also stems from a Kaluza-Klein reduction of a well defined higher dimensional metric theory. Properties of an asymptotically flat spherically symmetric black hole are analyzed, and new slowly rotating and radiating extensions are found. Through disformal transformations of the static configurations, gravitating monopole-like solutions and eternal wormholes are presented. The latter are shown to extract from spacetime possible naked singularities, yielding completely regular and asymptotically flat spacetimes.

gr-qc↗

arXiv2022

Invertibility conditions for field transformations with derivatives: toward extensions of disformal transformation with higher derivatives

We discuss a field transformation from fields $ψ_a$ to other fields $ϕ_i$ that involves derivatives, $ϕ_i = \bar ϕ_i(ψ_a, \partial_αψ_a, \ldots ;x^μ)$, and derive conditions for this transformation to be invertible, primarily focusing on the simplest case that the transformation maps between a pair of two fields and involves up to their first derivatives. General field transformation of this type changes number of degrees of freedom, hence for the transformation to be invertible, it must satisfy certain degeneracy conditions so that additional degrees of freedom do not appear. Our derivation of necessary and sufficient conditions for invertible transformation is based on the method of characteristics, which is used to count the number of independent solutions of a given differential equation. As applications of the invertibility conditions, we show some non-trivial examples of the invertible field transformations with derivatives, and also give a rigorous proof that a simple extension of the disformal transformation involving a second derivative of the scalar field is not invertible.

hep-th↗

arXiv2021

Deformed black hole in Sagittarius A

We analyze the post-Newtonian orbit of stars around a deformed Kerr black hole. The deformation we consider is a class of disformal transformations of a nontrivial Kerr solution in scalar-tensor theory which are labeled via the disformal parameter $D$. We study different limits of the disformal parameter, and compare the trajectories of stars orbiting a black hole to the case of the Kerr spacetime in general relativity, up to 2PN order. Our findings show that for generic nonzero $D$, the no-hair theorem of general relativity is violated, in the sense that the black hole's quadrupole $Q$ is not determined by its mass $M$ and angular momentum $J$ through the relation $Q=-J^2/M$. Limiting values of $D$ provide examples of simple and exact noncircular metric solutions, whereas in a particular limit, where $1+D$ is small but finite, we obtain a leading correction to the Schwarzschild precession due to disformality. In this case, the disformal parameter is constrained using the recent measurement of the pericenter precession of the star S2 by the GRAVITY Collaboration.

gr-qc↗